I had this happen several times. I have cable Internet and there was a problem at the cable company with my speed dropping below the level needed for the video to work. Once they straightened that out on their end, it immediately started working. Maybe something to check. You can run a speed test on-line yourself. If you don't know how or where, just Google Internet speed test. Good luck.
It is pretty difficult to troubleshoot if you're not around. However, if there is someone at home then perhaps they can help you troubleshoot.
If your the Slingbox isn't displaying a picture, it is possible the set-top isn't providing a signal. I would recommend testing the connectors from the cable box to see whether or not they're working. It is possible that the set-top box has Selectable Output Control (SoC) enabled, which is a part of High-bandwidth Digital Content Protection (HDCP). If your set-top box is also connected so another device using HDMI then its probable that it has disabled its own analog outputs.
There's more information and a possible workaround in the articles below.